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  • Mathematics
  • Introduction

Harvard Griffin GSAS strives to provide students with timely, accurate, and clear information. If you need help understanding a specific policy, please contact the office that administers that policy.

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Questions about these requirements? See the contact info at the bottom of the page. 

The First Two Years

The first year is a time to get to know Harvard, the faculty, and fellow students. This is a time to get a sense of what sort of mathematics is done here, at what level, in what style, and by whom. By the end of the first year, it should be possible for the student to have some idea of the area that is most interesting to them and with whom they might work.

While preparing for the qualifying examination or immediately after taking it, the student should enroll in more advanced courses with the idea of choosing a field of specialization. Most students choose a dissertation advisor during their second year or earlier. It is not usually a good idea to wait longer than two years before doing so. One method of choosing a professor with whom to work is to spend a term reading under the direction of two or more faculty members simultaneously on a tentative basis. Faculty members vary a great deal in the way that they go about dissertation supervision; one’s needs in that direction should be taken into account. 

The director of graduate studies and the department chair are available for consultation about choosing an advisor or to help with resolving other issues that might arise.

The Qualifying Examination

The examination is given twice each year: at the beginning of the fall and spring terms. Students are required to take the qualifying examinations (quals) in the fall term of the first year. The qualifying exam consists of three three-hour papers held on consecutive afternoons. 

The department offers a basic sequence of mathematics courses for the first two years in residence, which covers much of the qualifying exam syllabus. A qualifying examination syllabus and samples of prior exams and solutions are available on the department’s website .

A student may take the qualifying examination any number of times beginning in the first term. Students are expected to pass the examination by the end of the second year in residence in order to begin real mathematical research.

It is extremely rare for a student not to pass the qualifying examination by the third year. 

The department does not have a prescribed set of course requirements, but the University requires a minimum of two years of academic residence for the PhD degree.

Please see Enrolling in Courses  for relevant processes. 

The Minor Thesis

For the minor thesis, students choose a topic outside their area of expertise and, working independently, learn it well and produce a written exposition of the subject. The exposition is due within three weeks—or four, if the student is teaching. The minor thesis must be completed before the start of the third year in residence.

The topic is selected in consultation with the student's chosen faculty member other than the student’s PhD dissertation advisor. The topic should not be in the area of the student’s PhD dissertation. (For example, a student working in number theory might do a minor thesis in analysis or geometry.) At the end of the allowed time, the student will submit to the faculty member a written account of the subject and be prepared to answer questions on the topic.

The minor thesis is complementary to the qualifying exam. In the course of mathematical research, the student will inevitably encounter areas in which they are ignorant. The minor thesis is an exercise in confronting gaps of knowledge and learning what is necessary efficiently.

Language Requirement

Mathematics is an international subject in which the principal languages are English, French, German, and Russian. For the PhD, every student is required to acquire an ability to read mathematics in one of these three foreign languages. The student’s competence is demonstrated by passing a two-hour written examination. Usually, the student is asked to translate into English a page of text from a mathematics book or journal. Students may, if they wish, use a dictionary. If another language is specifically appropriate to the student’s PhD program, the student may request approval from the director of graduate studies to substitute that language. If a student has studied undergraduate mathematics in a language other than English, the student may request to have the language requirement waived.

The language requirement should be fulfilled by the end of the second year.

All graduate students are required to gain at least two terms of classroom experience in teaching. Teaching may be a source of support for some students. Students without outside support are usually required to teach once in each of years two through five.

Teaching fellows ordinarily prepare and teach their own sections of undergraduate calculus. Participation in course-wide meetings, examination writing, grading, and holding office hours are also part of the duties, but routine homework grading is done by a course assistant. There are a few upper-level tutorial seminars taught by experienced teaching fellows.

All students must complete Mathematics 300: Teaching Undergraduate Mathematics and an apprenticeship program run by the department in a term before they start teaching. Students usually complete the course in their first term and the apprenticeship during their first year.

AM Degree (Master's in passing)

The master of arts (AM) degree is not a prerequisite for the PhD degree but may be obtained by students on their way to a PhD. The formal requirements for the continuing AM degree are a minimum academic residence of one year and eight four-credit courses in mathematics at the 100 or 200 level, with at least four at the 200 level, and candidates must pass the language examination.

Applicants are accepted into the PhD program only; the department does not offer a terminal AM degree in mathematics.

The Remaining Years

The doctor of philosophy (PhD) is awarded to students who have demonstrated their mastery of the basic techniques of mathematics and their ability to do independent research. The former is tested in the qualifying examination, the latter in the dissertation. The dissertation, however, is the more important of the two.

The University requires a minimum of 2 years’ academic residence (16 4-credit courses). On the other hand, the PhD usually takes four to five years.

The Dissertation

The PhD dissertation is an original treatment of a suitable subject leading to new results, usually written under the guidance of a faculty member. Many of the more advanced courses and seminars are designed to lead the student to areas of current research.

Traditionally, dissertation defenses are held in March and April for a May degree. Degrees are conferred three times during the year—in November, March, and May, but most students finish for the May degree. The University Commencement is held in May.

Dissertation presentations are scheduled some weeks prior to the University dissertation submission deadline date. A final draft of the dissertation must be placed in the Birkhoff Library two weeks prior to the advisor’s dissertation report to the faculty. The student should consult their advisor regarding the selection of the dissertation committee. The student’s advisor presents the dissertation to the faculty during the departmental meetings that coincide with the timetable of the University.

Once the faculty members agree the dissertation can move forward, the student may proceed with their oral defense. The oral defense will be in the style of a seminar with a public presentation of about 50 minutes with 10 minutes for questions. The student’s dissertation committee members will attend the defense and formally approve the dissertation.

When the dissertation is accepted, the student can submit the dissertation to the registrar. The final manuscript must conform to the requirements described online in the Harvard Griffin GSAS policies. 

Contact Info

Mathematics Website  

Explore Events

  • Conferences
  • Guide to graduate study
  • The qualifying exam
  • The qualifying exam syllabus
  • Some old qualifying exams

How to obtain copies of past PhD theses

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Professional Development

Mathematical job search sites.

  • Senior faculty research interests
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  • The online application for 2016 admissions to the Department of Mathematics will be available on the Graduate School of Arts and Sciences Web site in late August 2015. GSAS Apply .

Graduate School of Arts and Sciences
Harvard University
Phone: (617) 495-5396
E-Mail:

Graduate Program Administrator
Susan Gilbert
(617) 496-5211
E-Mail:
The department strongly recommends applicants to seek out and apply for all sources of financing available to them for graduate study. Recommended sources for funding US graduate students are and . Applicants from the UK are urged to also apply for the and applicants from UK, New Zealand, Canada and Australia for . International students may apply for the or any home country fellowships available for study abroad.
A list of courses offered by the Mathematics department can be found .

The Harvard University School of Engineering and Applied Sciences (SEAS) offers programs for both the Master's degree and the PhD degree in Applied Mathematics. Please visit the SEAS Web site for more information on degrees in applied mathematics.


Guide To Graduate Study

  • Acquiring a broad basic knowledge of mathematics on which to build a future mathematical culture and more detailed knowledge of a field of specialization.
  • Choosing a field of specialization within mathematics and obtaining enough knowledge of this specialized field to arrive at the point of current thinking.
  • Making a first original contribution to mathematics within this chosen special area.

The Qualifying Exam

The qualifying exam syllabus, past qualifying exams.

Some old departmental qualifying exams are available here
(all links are PDF's)

(with Sol)
and
and
and
and
and
  • C* algebras
  • probability
  • algebraic geometry
  • differential topology
  • representation theory
  • algebraic topology
  • banach spaces
  • fluid mechanics
  • combinatorics
  • foundations
  • measure theory
  • commutative algebra
  • galois theory
  • noncommutative rings
  • universal algebra
  • complex analysis
  • game theory
  • numerical analysis

Teaching Requirements

Requesting Letters of Recommendation

Writing papers and submitting them.

  • Kleiman's notes on mathematical writing

Applying for jobs

  • Joe's guide to job searching and job talks
  • AMS guide to job searching
  • Tex package

Writing a CV

  • Example 1 and template (courtesy of Hank Zee)
  • Example 2 and template with style file (courtesy of Hank Zee)

Writing a Cover Sheet

  • The AMS guide to cover sheets , including templates in all formats




Senior Faculty Research Interests

Noam D. Elkies Professor of Mathematics Number theory, computation, classical algebraic geometry, music
Dennis Gaitsgory Professor of Mathematics Geometric aspects of representation theory
Robin Gottlieb Professor in the Teaching of Mathematics
Benedict H. Gross George Vasmer Leverett Professor of Mathematics Algebraic number theory, Diophantine geometry, modular forms
Joseph Harris Higgins Professor of Mathematics Algebraic geometry
Michael J. Hopkins Professor of Mathematics Algebraic topology
Arthur Jaffe Landon T Clay Professor of Mathematics and Theoretical Science Analysis, probability, symmetry, and geometry related to quantum and statistical physics
Mark Kisin Professor of Mathematics Number theory and arithmetic geometry
Peter Kronheimer William Caspar Graustein Professor of Mathematics Topology, differential and algebraic geometry, and their applications
Jacob Lurie Professor of Mathematics Algebraic geometry, algebraic topology, and higher category theory
Barry Mazur Gerhard Gade University Professor Number theory, automorphic forms and related issues in algebraic geometry
Curtis T. McMullen Maria Moors Cabot Professor of the Natural Sciences Riemann surfaces, complex dynamics, hyperbolic geometry
Martin Nowak Professor of Mathematics and Biology Mathematical biology, evolutionary dynamics, infectious diseases, cancer genetics, game theory, language
Wilfried Schmid Dwight Parker Robinson Professor of Mathematics Lie groups, representation theory, complex differential geometry
Yum-Tong Siu William Elwood Byerly Professor of Mathematics Several complex variables
Shlomo Sternberg George Putnam Professor of Pure and Applied Mathematics Differential geometry, differential equations, Lie groups and algebras, mathematical physics
Clifford Taubes William Petschek Professor of Mathematics Nonlinear partial differential equations and applications to topology, geometry, and mathematical physics
Hugh Woodin Professor of Philosophy and of Mathematics Set theory, determinacy, and strong axioms of infinity
Horng-Tzer Yau Professor of Mathematics Probability theory, quantum dynamics, differential equations, and nonequilibrium physics
Shing-Tung Yau William Caspar Graustein Professor of Mathematics Differential geometry, partial differential equations, topology, and mathematical physics
PhD dissertations are listed in descending order by year, author, and title . All scholars can order copies of most Harvard dissertations from 1982 to the present by contacting UMI/ProQuest at 1-800-521-3042. Permission of the author is usually required to copy theses within the last five years.

Most PhD dissertations submitted from March 2012 forward are available online in . Access to Harvard theses/dissertations that are not available through ProQuest depends on the school of origin and its associated library. Check the to see where a thesis is housed.

Harvard affiliates with IDs and PINs can access the full text of most Harvard PhD theses since 1990 from the .

Birkhoff Library

library. Books may be removed for photocopying, but they cannot be checked out or taken to offices. The Cabot library, located on the first floor of the Science Center, has a much larger collection of mathematics books and journals that be checked out. and in the library card catalog. There is a new section with books on calculus and math education near the computer. and related databases like . Please do not use this computer for non-library purposes (like email, etc.) General use computers are located on the first floor of the Science Center. (nancy@math) is the librarian. Ms. Miller's office is located inside the library. Please direct your questions and report missing books to her.

Photos and Media

  • PhD Timeline

--> Also see the separate pages with on-boarding information for new PhD students <--   Information and Resources for New Graduate Students Wiki site for incoming PhD students (behind Harvard Key)

First Year (G1)

  • Notify your financial aid officers of any external funding. Contact:  Erin Bishop  in SEAS Finance and  Emily Fingerle  in GSAS Financial Aid.
  • Make note of the course registration deadline. (previously known as "Study Card Day"). See the GSAS Policies  Academic Calendar.
  • Register for courses before the deadline  (previously known as "Study Card Day")
  • Mid-January: Deadline for submitting materials to be reviewed at the January CHD meetings .
  • Late-January: Course registration deadline (previously known as "Study Card Day").
  • G1s: Your  Prospective Program Plan  due to the Office of Academic Programs on this day.
  • Transfer of up to 3 classes of coursework may be allowed. Include the  Application for Credit for Work Done Elsewhere  with your Prospective Program Plan. 
  • April 1:   Research Advisor Selection Form /Research Assistant appointment form due to Office of Academic Programs.
  • Note: The April CHD meeting is the last CHD meeting in all academic year. CHD does not meet over the summer. Remember to plan ahead.

Second year (G2)

Throughout year.

  • G2’s are required to serve as a Teaching Fellow in either the Fall or Spring semester.
  • Make sure you complete the  TF form once you line up a TF position! 
  • G2’s are required to take their qualifying exam in either the Fall or Spring terms.
  • Email quals_defenses@seas  to book a room. If you book your own room (e.g., external to SEAS) you must still email  quals_defenses@seas  well in advance in order for your required documentation to be ready, else your exam cannot take place.
  • Upon completion of the exam, students are required to submit the  Designation of Research Committee  form to OAP.
  • If you plan to request a delay of the qualifying exam, complete a  Request to Delay Qual Exam  form. Note that delays until September (i.e. start of G3 year) are typically approved as a matter of course
  • Mid-September: Course Registration Deadline (previously known as "Study Card Day"). See the GSAS Policies  Academic Calendar.
  • Mid-October :  Final Program Plan  due to OAP; see the  CHD page  for dates.
  • Late-January : Course Registration Deadline (previously known as "Study Card Day"). See the GSAS Policies  Academic Calendar.
  • May 1 : Advising Agreement form due to OAP.
  • May:   Commencement and diploma options for Masters en Route / Continuing Master’s students - You can apply to receive your S.M. degree en route to your PhD after you have completed eight of your core courses (this requirement may depend on area). You will receive your S.M. diploma, and participate in the Commencement if you choose to. However since you will be considered a non-terminal degree recipient, you will not be able to join the ceremony in Sander's Theater. 

Third year (G3+) and beyond

  • Meet with your Research Committee at least annually, as indicated by your area's expectations.
  • Send any changes to your Final Program Plan to the CHD for review. See the  CHD page  for submission dates.   Note that   the Committee on Higher Degrees expects students not to petition for a revised Program Plan less than a year prior to the final defense  in case additional coursework is required, so it's important to keep your plan up to date with your courses as actually taken.
  • Inform OAP of any  changes to your research committee . 
  • PhD candidates can review their eligibility to receive an SM en route . 
  • Early-September:  Course Registration Deadline (previously known as "Study Card Day"). See the GSAS Policies  Academic Calendar.
  • Late-January: Course Registration Deadline (previously known as "Study Card Day"). See the GSAS Policies  Academic Calendar
  • May 1 :  RA reappointment  form due to OAP.

Completing your degree

Degree application.

  • Check out FAS degree-completion information  here  (Registrar) and deadlines  here  (GSAS calendar)
  • Complete the  degree application  via my.harvard by the Registrar's deadline.
  • If you schedule your own room (e.g., external to SEAS) you must still email quals_defenses@seas   well in advance in order for your required documentation to be ready,  else your defense cannot take place.   You must also get agreement from your full committee to hold your defense in a non-SEAS room.

Dissertation Submission and Commencement

  • The best way to share your dissertation with others is by linking to the DASH copy. DASH uses persistent URLs and provides you with download statistics, and the DASH copy of your PDF will not include the signed Dissertation Acceptance Certificate (DAC). If you choose to post or share your PDF in some other way, you should remove the DAC page so that readers do not have access to the scanned signatures.
  • Get ready for commencement by updating your email and other contact information via  my.harvard.edu .

In Applied Mathematics

  • First-Year Exploration
  • Areas of Application
  • AM & Economics
  • How to Declare
  • Who are my Advisors?
  • Secondary Field
  • Senior Thesis
  • Research for Course Credit (AM 91R & AM 99R)
  • AB/SM Information
  • Peer Concentration Advisors (PCA) Program
  • Student Organizations
  • How to Apply
  • PhD Model Program (Course Guidelines)
  • Oral Qualifying Examination
  • Committee Meetings
  • Committee on Higher Degrees
  • Research Interest Comparison
  • Collaborations
  • Cross-Harvard Engagement
  • Clubs & Organizations
  • Centers & Initiatives
  • Alumni Stories

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How good do I actually have to be to get into a top graduate program from an average undergraduate program?

So, this is a question that I do not know much about. I might get called on not having done a ton of research on graduate school, but I am really curious about this. I am an undergraduate student of mathematics and I am certainly planning on pursuing a graduate degree. I have looked at the top schools of math and they are certainly what one would expect: MIT, Harvard, Princeton, Yale, etc.

My issue is this: Academically, I was a late bloomer. I did not take high school seriously because it was annoying and elementary. Where I grew up, my school did not offer much in terms of AP classes or other opportunities. So, the only thing I excelled at naturally was math classes. Of course, they were extremely easy and required almost no effort on my part, which is what made me leery in terms of taking college level classes. I figured that I was good at high school classes because they are simple, but college level will be a different story.

I was wrong. In university, the gap was wider. Once I became adjusted, I actually enjoyed mathematics because it was so much more abstract and complex. This caused me to do rather large amounts of independent research in graduate level topics (topology, analytic number theory, analysis, etc). My only issue is that I am not in a competitive environment, really. The students are not top-notch, and don't share the same drive that I have. This is why I feel like being at the top of the class is not really an accomplishment, since I am not doing anything that any undergraduate at MIT, Harvard, Yale, etc, couldn't do.

My question that I pose here is this:

How good do I really need to be?

I have a passion for mathematics and for the most part, I seem to be talented at it. In terms of GPA, I have maintained a 4.0 with little effort just because I typically have already covered the material in the class on my own. However, there is a voice in the back of my head that keeps telling me that I only stand out because I am at a school that is not top tier, ivy league.

What does a graduate student at a top tier school look like? In my mind, I see someone that has been publishing papers since their teens, and was at the level I'm at now coming out of high school (I am a rising senior at the moment). Is this true? Am I being realistic? I am concerned because I would love to apply to some of these schools (and to get in is my dream!) but I honestly don't even know what level I am at in comparison to the rest of their applicants. I would hate to get shot down almost instantly because I am a joke in their eyes.

Sorry if this was a bit of a ramble. The question boils down to the title really, the rest is just elaboration for those that are interested. Thanks!

  • graduate-admissions
  • graduate-school

David Ketcheson's user avatar

  • 13 ... ivy league. — Don't worry about which athletic conference the school's sports teams play in. –  Mad Jack Commented Apr 22, 2015 at 23:42
  • 3 Is the question how good at math I have to be, or how good does my application need to look? Either way, it is unlikely to be appropriate here. Also what is a "rather large amount of independent research in graduate level topics "? Does that mean you have papers in decent journals? Does that mean you have looked at grad level textbooks? –  PVAL Commented Apr 22, 2015 at 23:44
  • 1 And the question boils down to: HOW do I get in? What will help me more: Academics/Grades or proof of well roundedness/involvement/how good my application is. –  Rellek Commented Apr 22, 2015 at 23:52
  • 4 "there is a voice in the back of my head that keeps telling me that I only stand out because I am at a school that is not top tier, ivy league." As JeffE would say, Do not listen to the Impostor Syndrome! –  chipbuster Commented Apr 23, 2015 at 1:53
  • 21 The very very rare people who have been publishing since their teens (yes, they do exist) all imagine other people winning the Putnam in elementary school. Someday a precocious fourth-grader will win the Putnam; no doubt she'll worry about someone else winning the Fields Medal while still in the womb. –  JeffE Commented Apr 23, 2015 at 2:44

4 Answers 4

From what you have said about yourself, I think you're very well prepared for graduate school at a very good institution. There are always a few incredibly bright, very young mathematicians that fit the image you have in your mind of students at top tier universities. I know of a few myself. However a very large number of math graduate students are much like you (and I).

I had a very strong affinity for math as a young child but grew up in one of the worst academic environments in the US. A highly nontrivial amount of students in my area didn't graduate high school, even fewer went to college and fewer then even went to universities that were not the crappy local universities. I lucked out because one of the best high schools in the nation was in my area yet I didn't feel very challenged and more or less coasted along and didn't try. Ended up with a GPA of about 3.0 at the time of graduation. I even spectacularly failed statistics with a 40 or so from lack of effort.

Undergrad rolled around. I flourished in the environment: took lots of math classes, took plenty of courses outside my degree to broaden my horizon, did lots of research, but like you I was a big fish in a small pond. I felt similar to you - that I only looked good in comparison to all of the others. I almost had a 4.0 in math and had a 3.8 overall with a couple of years of research under my belt. When it came time for grad school applications, I cast a bit of a wide net, but got rejected from a lot of universities. (This was largely my fault since I seemed to mess something up on every application. Having not really done undergraduate applications, I was a bit overwhelmed and scatterbrained.) I actually got into my top choice university which surprised me a lot.

When I started my master's, I did notice that there was a bit of a gulf between me and the other students once I got there. My undergraduate institution didn't have nearly the course selection or resources that the other students had. However in terms of math capability, I was at least middle of the pack; so while I had a bit of a learning curve and some growing pains, I think I ended up being one of the stronger master's students because I fully dedicated myself and didn't give up. I did spend a ridiculous amount of time in my office the first semester, though. I went to school around 9:30 in the morning and went home at midnight many days.

For all of it, I grew incredibly and am doing quite well in my PhD program. Coursework is a cinch now, research is going well and I'm writing up a couple of papers which I hope to submit in the not-too-distant future. With your background and love for mathematics, I think you'll be in a much better position than I was in terms of applications. Your GPA is better, you seem much more fluent in many areas of mathematics and are much more mathematically mature. The biggest factor in determining your success (outside of pure genius - which is incredibly uncommon, even amongst mathematicians!) is your unwillingness to give up. Even if you're slightly weaker than some of your future fellow graduate students right now, once you get there, all of those disparities will quickly melt away if you put in the time and effort. Where you came from does not have to dictate where you end up. You are more than your past if you allow yourself to be.

Here is some general off-topic advice regarding grad school since you seem to be lacking in advising: just because you want to go to a top tier university and get in to one does not mean you should necessarily go. For undergrad, this is not the case; if you get into MIT, Stanford, Harvard, etc. and have the financial means, you should definitely go as it is a great opportunity and can directly impact your future. At the graduate level, things are so much more nuanced. (For example, the reputation of the university doesn't directly dictate your future success provided that you put in 100%. In the internet age, it is much easier to do really meaningful research and network with top researchers at any respected university since you have access to all of the information you want.)

When you apply, you are not applying to the university more than you are applying to a professor (or professors) or at least this is the philosophy I think one should have. You should have an idea of what kind of things you want to pursue for research and you should look to those people who do research in that direction. I don't mean to say that you need to know exactly the project you want to do but have a rough idea of the field you are interested in, say commutative algebra or functional analysis or harmonic analysis. If you apply to a university in which no one really pursues what interests you, you're going to be without a future advisor or you'll have to settle for second best. Applying to a graduate program just because of prestige doesn't guarantee success or happiness. Granted, at the top universities, this tends not to be an issue as they have very broad reach but it is something to be wary about. Just because it is a great university or great department does not mean it is a great fit for you.

There are also other factors to consider when applying to schools: Could you deal with the super competitive atmosphere (or alternatively the extremely laid back atmosphere)? Could you stand to live there for four to six years, e.g. if you're from a very hot climate, could you survive the very harsh winters in upstate NY or if you're from upstate NY, could you handle a Texas summer? If you cannot see yourself being happy with (or tolerating) a lot of these extra-academic aspects of where you are, you might want to reconsider.

A PhD is very demanding and can be soul-crushing at times. You'll often run into really difficult road blocks in coursework or research and if everything else in your life makes you miserable as well, you're going to have a really bad time. Your mental health is very important. You will be pushed to the extreme at times and in many ways throughout your PhD and your environment shouldn't amplify this. If you're having a tough time in research, the weather is absolutely miserable and you cannot stand your fellow graduates for whatever reason, your mental wellness might take a turn for the worst. I have seen this happen first hand and it is really unfortunate. These are not things academic advisors often tell students who wish to do graduate school because they are easy to overlook, but it is something to keep in mind. Hopefully this has been helpful.

Cameron Williams's user avatar

  • This is a great comment. I honestly did not think about the extra-academic aspects such as weather. I really do hate the cold, and it seems like all of the top 10 schools are northern! And I like your perspective on applying to schools for some professor. I have not done enough research on this, since my books are all pretty old (Dover is cheap!) and I honestly have no idea who the big shots in mathematics are nowadays. I will definitely look into this, because I think you are very right about the importance of that. –  Rellek Commented Apr 23, 2015 at 12:40
  • 1 +1 for the last two paragraphs. those are certainly valid for other fields, too. –  henning no longer feeds AI Commented Apr 23, 2015 at 18:33

well I'm an MIT pure math PhD. I published my first paper when I was 27 : a couple of years after getting the PhD! Very few people has published anything before their PhD and their first paper generally was from their thesis.

If you have actually done some original research, write it up and get some advice from a professor at your school regarding publishing it. Being published is a massive help in grad school applications.

My general rule is only do a maths phd if you have a calling for it. It sounds like you do. I treated most of Grad School like a job -- go in around 9, take a break for lunch, go home around 6pm. Work hard during those hours. Enjoy your evenings and weekends.

High quality institutions do help your career so apply and if you get in, go and visit. If you don't like the atmosphere, go elsewhere. Certainly when I was at MIT the atmosphere was collegial rather than competitive.

Mark Joshi's user avatar

  • _Being published is a massive help in grad school applications. _ - Would you say this applies to patents too? aren't they a kind of "publication"?. Obviously we would not be talking about mathematics (a patent in mathematics, that would be interesting), but engineering. –  Keine Commented Apr 23, 2015 at 7:38
  • Thank you for commenting. It is nice to hear something from someone that is actually in a spot that I am yearning for, and this has made me feel much better about the situation. –  Rellek Commented Apr 23, 2015 at 12:36

Let me offer some perspective from an admissions point of view. What's important, for graduate studies, is your preparation, talent, motivation and work ethic. How will a committee assess this? If you go through a bunch of advanced courses with all A's from a top school, unless something is really wrong with your application, you'll get into a top school because the admissions people know the quality of the program you went through.

The main problem with coming from a small/unknown school (and I also did myself, so I'm sympathetic) is that it is harder to evaluate your preparation and talent, so to get into top programs there needs to be something in your application to gauge you against other applicants. Being able to do this is also helpful for personally knowing how you stack up with students coming out of top schools. Here are some suggestions:

  • Even if you're not at a great school, you probably have some professors who got their PhDs from top schools. They will have a sense of how you compare to students from top schools. Consequently, they will be able to give you informed advice about what kind of schools you should apply to, and be able to write in their recommendation letters things like "Rellek is comparable to the better students I've known at at Ivy League Institute, Inc." Note: recommendation letters are particularly important when you come from an unknown school.
  • If you've done things like summer programs with students from all over, your experience there can help gauge you against other students. (So it's natural to ask someone from one of these programs for a letter.)
  • If you've written research papers or typed up notes on advanced topics, you can make them available (say on a personal webpage), so interested committee members have the option of taking a look.
  • Consider applying to some backup schools and/or master's programs as backups. After a master's at a good school, you will be easy to compare with top students around the country.

As a final comment, it's true that to get into Harvard or Princeton, you should to be exceptional (or really lucky), but you merely need to be good and show promise to get into a top 10 school. I remember I was surprised when I found out most grad students I met at top 10 schools weren't "superstars" (some are, of course, but that's not par for the course).

Kimball's user avatar

If you state on your letter of purpose what you have stated here, it will be regarded highly, because the admissions officer will see the passion that you have, and that has more relevance than anything.

Opportunity doesn’t knock. If it knocks, it knocks on the inside.

You.... are opportunity… You create it

And...You are what you believe.

That is what sets you apart, and, that is what you need to let these Ivy League admissions people know.

That is what I did...

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harvard math phd application

College of Arts and Sciences

Mathematics, graduate programs.

Math graduate student at Lehigh University

Mathematics is one of the fundamental, most unified and universal sciences. The discipline of mathematics trains the mind to use logic and reason to discover new knowledge and to make sense of what we already know.

Graduate degrees offered:

M.S. in Mathematics

Ph.D. in Mathematics

M.S. in Applied Mathematics

Ph.D. in Applied Mathematics

M.S. in Statistics and Data Science

Students in our Ph.D. in Applied Mathematics program may also choose to pursue research in Statistics. Our Ph.D. degrees are research-based. There is no research requirement for our M.S. programs.

For more information, call (610) 758-3730 or contact the Graduate Committee at [email protected] .

M.S. in Mathematics, Applied Mathematics, or Statistics and Data Science

The M.S. programs require 30 credit hours of graduate courses with at least 18 hours at the 400 level. With the permission of the chair, up to six hours of these courses can be replaced by a thesis. All M.S. students must also pass a comprehensive examination during their first year which covers calculus, differential equations, and linear algebra (Mathematics or Applied Mathematics) or calculus, linear algebra and probability and statistics (M.S. Statistics and Data Science).

The M.S. degree can serve both as a final degree in mathematics or as an appropriate background for a Ph.D.

Ph.D. in Mathematics or Applied Mathematics

The plan of work for the Ph.D. degree includes the Comprehensive Exam, described above, and Qualifying Examinations. Ph.D. in Mathematics students will all take the Qualifying Examination in the same two areas, Algebra and Real Analysis, within two years. Students in the Ph.D. in the Applied Program will follow a parallel policy and be tested on two different areas, Statistics and Applied Probability for students in the Statistics track and Analysis and Differential Equations for students in the Applied Mathematics track. 

In addition, each student will be required to prepare a written plan for additional advanced course work and substantial reading of research articles. An Advanced Topic examination will also be required in the third year. A General Exam, in which the candidate describes the thesis program, and the doctoral dissertation and its defense complete the work for the PhD degree. A student entering Lehigh without a Masters degree must take 72 credits including at least 48 regular course credits (i.e. not dissertation credits). These students typically earn their Masters degree during the process of their work. A student entering Lehigh with a Masters degree must take 48 credits including at least 18 regular course credits (i.e. not dissertation credits).

Financial support

We offer financial support to Ph.D. students through a combination of teaching assistantships, research assistantships, and fellowships.

Explore the Graduate Programs

Student spotlight.

Ningxi Wei discusses her research and experience in Lehigh's Ph.D. in Mathematics program.

Computational Science and Engineering

Program finder image

Graduate Program

The Computational Science and Engineering (CSE) master’s program, led by faculty from Computer Science, Applied Math and the Engineering Sciences, provides rigorous training in the mathematical and computational foundations of CSE. The master’s program offers students experience with mathematical techniques for modeling and simulation of complex systems; parallel programming and collaborative software development; and methods for organizing, exploring, visualizing, processing and analyzing very large data sets.

  • Office of Graduate Education

Applicant FAQ

harvard math phd application

Frequently Asked Questions – Eligibility, Funding, Knight-Hennessy Scholars, etc.

In addition to the most frequently asked Biosciences questions below, please also visit the Graduate Admissions FAQ web page for a more expansive list.

Are there any prerequisites or background coursework required for the 14 Biosciences PhD Programs?

A majority of the Biosciences PhD Programs do not have specific course requirements for admission.  The faculty like to see that you have taken a rigorous course load, but they will be particularly interested in your research experience.  While many of our graduate students have undergraduate preparation in a life sciences curriculum, it is feasible to enter from other programs, including chemistry, computer science, mathematics, psychology, or physics.  The  Biomedical Data Science ,  Biophysics ,  Molecular and Cellular Physiology , and  Structural Biology  programs have prerequisite or background course requirements. We strongly recommend that you reach out to the  programs  to which you plan to apply, to ask for specific course requirements/suggestions.

Can I apply to other graduate programs (e.g. Applied Physics, Bioengineering, Chemistry, Computer Science, etc.) in addition to the 14 Biosciences PhD Programs?

You may apply to only one graduate program per academic year. The only exception is within the 14 Biosciences PhD Programs, where you may apply for two Biosciences programs within a single application. The 14 Biosciences PhD Programs include:

  • Biochemistry
  • Biomedical Data Science
  • Cancer Biology
  • Chemical and Systems Biology
  • Developmental Biology
  • Microbiology and Immunology
  • Molecular and Cellular Physiology
  • Neurosciences
  • Stem Cell Biology and Regenerative Medicine
  • Structural Biology

Can I defer my enrollment?

Admitted students are expected to enroll in their Home Program in September of the year they are admitted. Deferral requests will be reviewed by your admitting program’s admissions committee and are approved on a case-by-case basis. The maximum length of an admissions deferral granted by Stanford is one year. Typically, deferral requests are only approved for military, medical, visa, or education-related purposes.

Can recommenders submit their letter via mail, email, fax, or a letter service?

All recommendations must be submitted using the online application system as recommenders are required to respond to specific evaluation questions on the recommendation form. Letters of recommendation cannot be mailed, emailed, faxed, or submitted through a letter service (with the exception of Interfolio). For letters submitted via Interfolio, please remember that letters written specifically for your Stanford graduate program tend to be stronger than letters written for general use purposes.

Do any of the 14 Biosciences PhD Programs offer an MS degree program?

The Biomedical Data Science program is the only Biosciences Program that currently offers an MS degree program.  Information about the program and its application process can be found on its website .

If you are not interested in one of the 14 Biosciences PhD Programs, you can find a list of all the currently offered degrees at Stanford (along with their contact information) on the Graduate Admissions  Explore Programs web page .

Do I need to hold an MS degree to be eligible to apply?

A Master’s degree is only required if you do not meet the following eligibility requirements.  To be eligible for admission to graduate programs at Stanford, applicants must meet  one  of the following conditions:

  • Applicants must hold, or expect to hold before enrollment at Stanford, a bachelor’s degree from a U.S. college or university accredited by a regional accrediting association.
  • Applicants from institutions outside the U.S. must hold, or expect to hold before enrollment at Stanford, the equivalent of a U.S. bachelor’s degree from a college or university of recognized standing. See the Office of Graduate Admissions for the  minimum level of study required of international applicants .

Do I need to include a department code number when requesting to have my GRE and/or TOEFL scores sent to Stanford?

Applicants should have the Educational Testing Service (ETS) send scores electronically to Stanford. Our university code is  4704  and no department code is required. You will either self-report your scores or indicate the date you will take the test(s) in the online application. Self-reported test scores will be used by the relevant admissions committee in their initial review process. Your unofficial test scores will be validated when your official scores are received by the University.

Do I need to secure a Lab/Thesis Supervisor prior to applying?

You will not need to secure a research supervisor prior to applying. Incoming students usually do 2-4 lab rotations during their first year.  Information on the rotation process can be found on the following  website .  If you realize a few weeks into a rotation that the lab is not a good fit for you, then there is no reason for you to stay any longer.

Do I need to submit official transcripts/academic records?

Graduate Admissions only requires admitted applicants who accept the offer of admission to submit official transcripts that shows their degree conferral. More details on this can be found on the following Graduate Admissions  webpage .   Please do not send or have sent any transcripts to us or to your program. 

Do you offer fellowships to international applicants?

We have a limited number of fellowships (which include a yearly stipend, tuition, and health and dental insurance) available to the most highly competitive international applicants. The stipend for the 2023-24 Academic Year is $51,600 ($12,900 per quarter). Admittance to the Biosciences Programs for international applicants varies from year to year depending on funding and available space. We strongly encourage applicants to apply for scholarships/fellowships in their home country that can be used overseas. Some useful websites that include information on external fellowships are:

  • Fulbright Foreign Student Program
  • The Fogarty International Center at the NIH
  • International Center at the Institute of International Education (IIE)

Applying for scholarships/fellowships generally takes some time to arrange, so plan ahead. You will be able to list any scholarships/fellowships that you have applied for and been awarded in the “Additional Information” section of the online application under “External Funding for Graduate Study”.  For more information about the costs and estimated expenses of attending Stanford, please visit the following  webpage .

Does the Bioengineering PhD program participate in the Biosciences Interview Session?

The Bioengineering PhD program is not one of the 14 Biosciences PhD Programs and has a separate admissions process and Interview Session.

How do I change one of my recommenders?

On the Recommendations page of the application, click on the recommender’s name you wish to replace, then click Exclude at the bottom of the resulting popup window. You then will see the option to add a new recommender. The recommender you exclude will not receive an email notification.

How does the funding work for those admitted to the Knight-Hennessy Scholars Program and the Biosciences?

The Knight-Hennessy Scholars program funding covers the first three years and your admitting Home Program will cover the remaining years.

I previously applied to the Stanford Biosciences Programs and was not admitted. What application materials will I need to submit?

Applicants who wish to reapply follow the same application process as first-time applicants. Reapplicants have the option of using letters of recommendation from their prior submitted Biosciences application or having new ones submitted.  Prior applications from the Autumn 2022, 2023, and 2024 admission cycles have been retained. It is highly recommended that one new letter of recommendation be submitted on your behalf.  When completing the application, you will be required to enter the information for a minimum of three recommenders (including the information for the letter writers that you plan to reuse).

For the letters you plan to reuse, please notify your recommenders in advance that they will receive a recommendation request but should not take any action.  Once you submit your application, please submit an email to the Biosciences Admissions Office indicating which letters you would like to reuse so we can add them to your application.

I’m an applicant whose first language is not English. Is it possible to have the TOEFL Test requirement waived?

Information about the TOEFL Test requirements, exemptions and waivers can be found on the  Graduate Admissions  website. Please note that if you submit a waiver request, it will be routed to Graduate Admissions  after you submit your application . Allow up to 15 business days after submitting your application for a response.

I’ve applied to multiple Home Programs and was wondering what happens if more than one program is interested in interviewing me?

In that case, the admissions representatives confer and attempt to determine which Home Program best fits your interests and should serve as your host. They will use the information you provided in your Statement of Purpose and on the Biosciences Supplemental Form. In most cases the best match is clear, but in rare cases where this is not the case, an admissions committee member will contact you directly to discuss with you which Home Program would be the best to host your visit. You will also have an opportunity to meet with faculty affiliated with other Home Programs during your visit.

If my school does not use a 4.0 GPA grading scale, how should I report this on my application?

You are asked to enter both GPA and GPA scale for each institution you list on the application. Enter your GPA as it appears on your transcript. Do not convert your GPA to a 4.0 scale if it’s reported on a different scale.

Is there a minimum GPA requirement?

There is no minimum GPA requirement to be considered for admission. The application review process is holistic and all aspects of the application (prior coursework, letters of recommendation, the statement of purpose, prior research experience, and test scores {if applicable}) are considered by the Admissions Committee when making an admissions decision.

What if my recommenders are not receiving their recommender link emails?

Occasionally, some email servers will send recommender link emails directly to Spam or will not allow the email to reach the primary inbox at all (particularly for email addresses located outside of the United States). Please reach out to Technical Support by submitting a request via the “Request Application Support” button on the “Instructions” page of your application.

What is included in the offer of admission?

The offer of admission for the 2023-24 Academic Year included a stipend of $51,600 ($12,900 per quarter), health and dental insurance, and graduate tuition. The stipend and benefits for the 2025-26 Academic Year will be set sometime in March 2025.  For more information about the costs and estimated expenses of attending Stanford, please visit the following webpage .

What is the Knight-Hennessy Scholars program?

The  Knight-Hennessy Scholars  program develops a community of future global leaders to address complex challenges through collaboration and innovation. The program will award up to 100 high-achieving students with three years of funding to pursue a graduate education at Stanford. To be considered, you  must apply to both  the Knight-Hennessy Scholars by Wednesday, October 9, 2024, at 1:00 pm (PST) and to one of the Stanford Biosciences PhD programs by Sunday , December 1, 2024, at 11:59:59 pm (PST) .  Information about the program and the application process can be found on the  Knight-Hennessy Scholars  program website.

COMMENTS

  1. Admissions

    Admissions. Financial Support. Graduate Program Administrator. Marjorie Bell (she/her) 617-496-5211. [email protected]. Science Center Room 331. 1 Oxford Street. Cambridge, MA 02138.

  2. Harvard Mathematics Department Graduate Information

    The application deadline for fall 2024 admission has passed. Applications for fall 2025 admission will open in September 2024. For information on admissions and financial support, please visit the Harvard Harvard Kenneth C. Griffin Graduate School of Arts and Sciences. Harvard Griffin GSAS is committed to ensuring that our application fee does ...

  3. Overview of the PhD Program

    a Secondary Field (which is similar to a "minor" subject area). SEAS offers PhD Secondary Field programs in Data Science and in Computational Science and Engineering. GSAS lists secondary fields offered by other programs. a Master of Science (S.M.) degree conferred en route to the Ph.D in one of several of SEAS's subject areas.

  4. Mathematics

    Additional information on the graduate program is available from the Department of ... [email protected]. Phone. 617-495-2171. The Harvard Kenneth C. Griffin Graduate School of Arts and Sciences is a leading institution of graduate study, offering PhD and select master's degrees as well as opportunities to study without pursuing a degree ...

  5. Guide To Graduate Study

    Guide to Graduate Studies. The PhD Program. The Ph.D. program of the Harvard Department of Mathematics is designed to help motivated students develop their understanding and enjoyment of mathematics. Enjoyment and understanding of the subject, as well as enthusiasm in teaching it, are greater when one is actively thinking about mathematics in ...

  6. Mathematics

    The graduate Mathematics Program at Harvard is designed for students who hope to become research mathematicians and show definite promise in this direction. Once the student has demonstrated a command of basic mathematical concepts by passing the qualifying examination, the emphasis is on getting to the frontiers of some field by independent ...

  7. Apply

    Step 4: Complete your application by the deadline. The degree program application becomes available in September. You should review Applying to Degree Programs before starting your application. All components of the application to a degree program are due by 5:00 p.m., Eastern Time, on the deadline date. Applications for the Visiting Students ...

  8. Harvard Mathematics Department : Graduate information

    Undergrad. Graduate. Research. Admin. Events. Seminars. Conferences. Sitemap. Department of Mathematics FAS Harvard University One Oxford Street Cambridge MA 02138 USA Tel: (617) 495-2171 Fax: (617) 495-5132.

  9. Graduate Program Timeline

    Harvard Mathematics Department Graduate Program Timeline. Graduate Program Requirements Timeline. Year One. Students are expected to take the Qualifying Exam, take Math 300: Teaching Undergraduate Mathematics, and if they need to teach in the second year for funding, complete the teaching apprenticeship. Students must enroll in four courses per ...

  10. PhD in Applied Mathematics

    The application fee of $105.00. Should you want to request a fee waiver from Harvard Griffin Graduate School of Arts and Sciences, you may do so in the fee section of the application. Please list only SEAS ladder faculty on the application. "Affiliate faculty" cannot admit PhD students. There are many SEAS ladder faculty with formal joint ...

  11. Harvard Mathematics Department : Information

    The director of graduate studies is Mark Kisin, Science center, 2nd Floor, [email protected]. For question about graduate studies in Mathematics, contact the graduate program administrator Marjorie Bell. Director of Undergraduate Studies The director of Undergraduate Studies (DUS) is Cliff Taubes.

  12. PhD in Applied Mathematics

    Doctoral students may earn the masters degree en route to the Ph.D. Prospective students apply through Harvard Griffin GSAS; in the online application, select "Engineering and Applied Sciences" as your program choice and select "PhD Applied Math" in the Area of Study menu. The Applied Mathematics program does not offer an independent ...

  13. Applied Mathematics

    Research and educational activities have particularly close links to Harvard's efforts in Mathematics, Economics, Computer Science, and Statistics.. Why Pursue an Applied Math Degree? A degree in applied mathematics prepares students for a wide range of careers because it focuses on applying mathematical concepts to real-world problems, especially in fields such as business, technology, or ...

  14. graduate admissions

    0. Roughly: good grades (3.8+ GPA) in difficult courses, good test scores (80+ percentile on math GRE subject test [not the regular GRE math, which you should get a ~perfect score on without studying]), strong research background and good letters corresponding to it. That will get you into schools in the top ~30.

  15. Mathematics

    Mathematics is an international subject in which the principal languages are English, French, German, and Russian. For the PhD, every student is required to acquire an ability to read mathematics in one of these three foreign languages. The student's competence is demonstrated by passing a two-hour written examination.

  16. Harvard Mathematics Department Harvard Department of Mathematics PhD

    Department of Mathematics. Science Center Room 325. 1 Oxford Street. Cambridge, MA 02138 USA. Tel: (617) 495-2171 Fax: (617) 495-5132. Department Main Office Contact. Web Site Contact. Digital Accessibility. Legacy Department of Mathematics Website.

  17. Harvard Mathematics Department : Graduate Information

    The PhD program of the Harvard Department of Mathematics is designed to help motivated students develop their understanding and enjoyment of mathematics. Enjoyment and understanding of the subject, as well as enthusiasm in teaching it, are greater when one is actively thinking about mathematics in one's own way.

  18. AM PhD Model Program

    Students should also note the school's overall PhD Program Plan requirements. ... as MIT offers a different course selection than is available at SEAS and Harvard. Examples of MIT courses taken by Applied Math PhD students include 2.29, 6.252J, 6.851, 8.334, 16.920, 18.1021,18.335J, 18.336.

  19. Applied Mathematics

    Graduate. Harvard School of Engineering offers a Doctor of Philosophy (Ph.D.) degree in Applied Mathematics. Doctoral students may earn the masters degree en route to the Ph.D. Students are drawn to Applied Mathematics by the flexibility it offers in learning about how to apply mathematical ideas to problems drawn from different fields, while ...

  20. PhD Timeline

    Mid-January: Deadline for submitting materials to be reviewed at the January CHD meetings. Late-January: Course registration deadline (previously known as "Study Card Day"). G1s: Your Prospective Program Plan due to the Office of Academic Programs on this day. Transfer of up to 3 classes of coursework may be allowed.

  21. graduate admissions

    Harvard does not have an "applied mathematics" department or a "PhD program in applied mathematics." Rather, applied mathematics is one of seven "areas of study" in the school of engineering and applied sciences: see here .

  22. How good do I actually have to be to get into a top graduate program

    However a very large number of math graduate students are much like you (and I). ... Stanford, Harvard, etc. and have the financial means, you should definitely go as it is a great opportunity and can directly impact your future. At the graduate level, things are so much more nuanced. ... Applying to a graduate program just because of prestige ...

  23. PDF PhD Students Resumes

    by Harvard Graduate School of Arts and Sciences Business Club Boston, MA . Participant . ... • Pre-screened 400+ graduate program applications. ... I found your name through Firsthand Advisers and saw that you completed your PhD in Applied Math before beginning your work as a quantitative analyst. I will be completing my PhD in Biology at

  24. Graduate Programs

    Students in our Ph.D. in Applied Mathematics program may also choose to pursue research in Statistics. Our Ph.D. degrees are research-based. There is no research requirement for our M.S. programs. For more information, call (610) 758-3730 or contact the Graduate Committee at [email protected].

  25. Computational Science and Engineering

    Harvard Kenneth C. Griffin Graduate School of Arts and Sciences The Computational Science and Engineering (CSE) master's program, led by faculty from Computer Science, Applied Math and the Engineering Sciences, provides rigorous training in the mathematical and computational foundations of CSE.

  26. Applicant FAQ

    A Master's degree is only required if you do not meet the following eligibility requirements. To be eligible for admission to graduate programs at Stanford, applicants must meet one of the following conditions: Applicants must hold, or expect to hold before enrollment at Stanford, a bachelor's degree from a U.S. college or university accredited by a regional accrediting association.